The spread of disease through human populations is a complex phenomenon. The characteristics of disease propagation evolve with time, as a result of a multitude of environmental and anthropic factors. This non-stationarity is a key factor in this huge complexity. In the absence of appropriate external data sources, to correctly describe the disease propagation, we have proposed a flexible approach, based on stochastic models for the disease dynamics, and on diffusion processes for the parameter dynamics. Coupled with particle MCMC, this approach allows us to reconstruct the time evolution of some key parameters. Thus, by capturing the time-varying nature of the different mechanisms involved in disease propagation, the epidemic can be suitably described.

This framework could be particularly useful for dealing with a potential pandemic which would have characteristics that do not allow effective understanding of its propagation, for instance: silent transmission and/or a major time variation in the reporting of cases. The latter could occur due to lack of timely or appropriate testing, Public Health interventions and/or modification of human behavior during the epidemic. This original framework would enable us to reconstruct the time evolution of the transmission rate of the pathogen based purely on the available data without specific hypothesis on its evolution. Then we would follow both the course of this epidemic and the time evolution of its effective reproduction number. The interest of our approach would be of critical importance when deciding on mitigation factors and balancing health, societal and economic consequences of any proposed mitigation measures.